The complexity of comparability graph recognition and coloring

M. C. Golumbic

doi:10.1007/BF02253207

The complexity of comparability graph recognition and coloring

Research output: Contribution to journal › Article › peer-review

Abstract

Using the notion of G-decomposition introduced in Golumbic [8, 9], we present an implementation of an algorithm which assigns a transitive orientation to a comparability graph in O(δ·|E|) time and O(|E|) space where δ is the maximum degree of a vertex and |E| is the number of edges. A quotient operation reducing the graph in question and preserving G-decomposition and transitive orientability is shown, and efficient solutions to a number of NP-complete problems which reduce to polynomial time for comparability graphs are discussed.

Original language	English
Pages (from-to)	199-208
Number of pages	10
Journal	Computing (Vienna/New York)
Volume	18
Issue number	3
DOIs	https://doi.org/10.1007/BF02253207
State	Published - Sep 1977
Externally published	Yes

ASJC Scopus subject areas

Theoretical Computer Science
Software
Numerical Analysis
Computer Science Applications
Computational Theory and Mathematics
Computational Mathematics

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10.1007/BF02253207

Cite this

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abstract = "Using the notion of G-decomposition introduced in Golumbic [8, 9], we present an implementation of an algorithm which assigns a transitive orientation to a comparability graph in O(δ·|E|) time and O(|E|) space where δ is the maximum degree of a vertex and |E| is the number of edges. A quotient operation reducing the graph in question and preserving G-decomposition and transitive orientability is shown, and efficient solutions to a number of NP-complete problems which reduce to polynomial time for comparability graphs are discussed.",

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The complexity of comparability graph recognition and coloring

Abstract

ASJC Scopus subject areas

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